Among the descendants of the Latin word sic ("thus, so, or just like that"), only the Portuguese word sim ends with a nasal consonant. Actually, in modern Portuguese, it ends with a nasal vowel, [sĩ], which must have developed from [sim] by assimilation. Compare this with its "sister" words, taken from the Wiktionary, which have all dropped the final [k]:

• Aromanian: shi
• French: si, ainsi
• Italian: sì, così
• Romanian: și
• Spanish: sí , así
• Catalan: així

The closest word is the French (no surprise, given we are talking about nasalization) ainsi, which comes from Latin (ad) + in + sic. So where did this nasal at the end in Portuguese sim come from? Could it be a further development from French? Something like ainsi becoming assim (and later, sim), by metathesis?